Phase equilibrium data for the hydrogen sulphide + methane system at temperatures from 186 to 313 K and pressures up to about 14 MPa

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Phase equilibrium data for the hydrogen sulphide +

methane system at temperatures from 186 to 313 K and

pressures up to about 14 MPa

Christophe Coquelet, Alain Valtz, Paolo Stringari, Marko Popovic, Dominique

Richon, Pascal Mougin

To cite this version:

Phase Equilibrium Data for the Hydrogen Sulphide + Methane System at Temperatures from 186 to 313 K and Pressures up to about 14 MPa.

Christophe Coquelet1, Alain Valtz1, Paolo Stringari1, Marko Popovic1

Dominique Richon2,3 and Pascal Mougin4

1

Mines ParisTech, CTP - Centre Thermodynamique des Procédés, 35 Rue Saint Honoré, 77300 Fontainebleau, France. 2

Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Durban, 4041, South Africa. 3

Department of Biotechnology and Chemical Technology, Aalto University, School of Science and Technology, P.O. Box 16100, 00076 Aalto, Finland

4

IFPEN, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France

________________________________________________________________________ Isothermal vapour-liquid equilibrium data have been measured for the methane - hydrogen sulphide (CH4 + H2S) binary system at five temperatures from 186.25 to 313.08

K, and pressures between 0.043 and 13.182 MPa. The experimental method used in this work is of the static-analytic type, taking advantage of two pneumatic capillary samplers (Rolsi™, Armines' patent) developed in the CTP laboratory. The data were obtained with the following maximum expanded uncertainties (k = 2): u(T) = 0.06 K, u(P) = 0.006 MPa and the maximum uncertainty for compositions u(x, y) = 0.010 for molar compositions. The data have been satisfactorily represented with the classical Peng and Robinson equation of state.

Keywods: VLE and LLE data, High-pressures, Modelling, Hydrogen Sulphide, Methane.

____________________________________________________________________________________________________________

Corresponding authors:

Pascal.mougin@ifpen.fr, Telephone: (33) 147526625, Fax: (33) 147527064

Introduction

In the past three decades a number of sour natural gases and gas condensates fields have been discovered around the world. Some of these fields have been classified as heavy natural gases. Some of them contain great amount of sulphur compounds like hydrogen sulphide. In some cases, the amount of H2S can be greater than 30 molar

percent. Whatever the concentration over a defined value, it is necessary to treat such acid gases to eliminate all traces of toxic sulphur compounds before their uses. Regulation imposes that sweet gas must contain less than 4 ppmv of H2S. In most industrial plants,

the removal acid gases (H2S) achieved by chemical or physical absorption with solvent.

Petroleum industry needs reliable and accurate vapour-liquid equilibrium data for mixtures of hydrocarbons and hydrogen sulphide in order to develop accurate models for calculating thermodynamic properties of natural gases requested for plants designs. Hydrogen sulphide and methane are also present in other energy contexts: for example they are present in gases produced from coals or biomass products from which H2S must

be eliminated. H2S – methane binary system is very interesting for the petroleum

industry, then it is useful to have high accuracy experimental data on a large range of temperatures and pressures.

193 to 364 K, respectively. In the DECHEMA handbook [4], interaction parameter has been determined for this system using the Peng and Robinson equation of state (PR EoS) [5] with the classical mixing rule (kij = 0.08). This system can be classified as a type III

according to the classification of Scott and van Konynenburg [6]. This behaviour is confirmed by the data on the critical locus measured by Reamer et al. and Kohn and Kurata.

In this paper, we present new experimental data and their modelling with classical cubic equation of state. Measurements have been carried out at low temperature in order to complete the literature data. The Peng and Robinson Equation of state (PR EoS) is used with a constant binary interaction parameter and with a binary interaction parameter function of the temperature.

Experimental Section.

All the details concerning the chemicals used are presented in Table 1.

The apparatus used in this work is based on a “static-analytic” method with liquid and vapour phase sampling. It is similar (see Figure 1) to that described by Courtial et al. [7] and Théveneau et al. [8].

The equilibrium cell is immersed inside a regulated liquid bath (Lauda RUK 90). Temperatures are measured with two platinum resistance thermometer probes (Pt100) inserted inside the top and bottom parts of the equilibrium cell. They were calibrated against a 25-reference platinum probe (TINSLEY Precision Instrument) calibrated by the Laboratoire National d'Essais (Paris) following the 1990 International Temperature Scale protocol.

Huot). Pressure and temperature data are recorded on a computer connected to a HP data acquisition unit (HP34970A).

The data were measured at two different time periods and so two separate campaigns of measurement were done.

-For the first campaign, measurements were done at 223.17, 273.54 and 313.08 K. Two pressures transducers were used and selected in relation to the pressure ranges: 0–10 and 0-30 MPa. After calibrations, the expanded uncertainties (k=2) on pressures are not higher than u(P) = 0.0025 MPa and u(P) = 0.006 MPa respectively. The expanded uncertainty concerning the temperature is u(T) = 0.06 K.

-For the second campaign, measurements were done at 186.25 and 203.40 K. The pressure transducer was selected in relation to the pressure ranges: 0 – 15 MPa. After calibrations, the expanded uncertainties (k=2) are not higher than u(T) = 0.02 K and u(P) = 0.0025 MPa.

C) Experimental Procedure

At room temperature, the equilibrium cell and its loading lines are evacuated down to 0.1 Pa. The cell (volume of the cell around 31 cm3) is first loaded with liquid

H2S (about 5 cm3). Equilibrium temperature is assumed to be reached when the two Pt100

probes give equivalent temperature values within their temperature uncertainty for at the least 10 minutes. Also, equilibrium is assumed when the total pressure remains unchanged within  1.0 kPa during a period of 10 min under efficient stirring.

After recording the vapour pressure of the H2S (the heavier component) at the

equilibrium temperature, about ten P, x, y points (liquid and vapour) of the two-phase envelopes are determined. For this purpose methane (the lighter component) is introduced step by step, leading to successive equilibrium mixtures of increasing overall methane composition (T, P, x and y).

Besides constancy of T and P, it is necessary to check also for phase compositions constancy. For these purposes, various samples of phases are withdrawn using the ROLSITM pneumatic samplers [9] and analysed. When equilibrium is reached and

capillary purged the measured compositions remain constant within experimental uncertainty. Then for each observed equilibrium condition, at least five more samples of both vapour and liquid phases are withdrawn and analysed in order to check for the measurement repeatability.

Modelling by equation of state:

The critical temperatures (TC), critical pressures (PC), and acentric factors (), for

we have used the Mathias-Copeman alpha function [10] expressed in eq 1. With its three adjustable parameters it was especially developed for polar compounds.

 

2 3 3 2 2 1 1 1 1 1                                        C C C T T c T T c T T c T  (1)

When T>TC, Eq. 1must be replaced by Eq. 2,

 

2 1 1 1                    C T T c T  (2)

The three (c1, c2 and c3) adjustable parameters are reported in Table 3. For VLE

representation, we chose the Van der Waals mixing rules, i.e. :

i i i b



x b (3)



1



i j i j ij i j a



x x a a k (4)

The binary parameter k_ijcan be a constant or temperature dependent as expressed in Eq. 5 b ij a ij ij k k k T   (5)

The adjustment of the binary interaction parameter is performed through a modified Simplex algorithm [11] using the objective function:

                 



N cal P P P N F 1 2 exp exp 100 (6)

Where N is the number of data points, Pexp is the measured pressure (experimental

pressure value), Pcal is the calculated pressure through bubble point calculations. From

in very good agreement with experimental ones within our determined experimental uncertainties.

Results and discussion:

Tables 4 and 5 report our measurements. The repeatability of the measurements is better than 1%. At our lowest temperature (186.25 K), we observe a liquid – vapour equilibrium for the pressures up to 3.671 MPa and a liquid – liquid equilibrium for the higher pressures. The same behaviour is observed 203.40 K. For higher temperatures, only vapour – liquid phase diagrams have been observed in our experimental pressure range. Figures 2 and 3 show the experimental data at respectively 186.25 and 203.40 K and the curves calculated with the PR Model and binary parameters adjusted on our experimental data at these temperatures. The other data related to classical liquid – vapour behaviours are not drawn.

Table 6 gives the values of binary parameters for each temperature. This enables determining a temperature dependent binary parameter:

8.733 0.0523 / ij k T K   (7)

Finally, the new experimental data have been added to the literature ones and a new temperature-dependent expression for the binary interaction parameter was obtained for the whole ensemble of data:

12.30 0.0390 / ij k T K   (8)

The deviations on pressures and compositions are given in table 7.

In this section, absolute deviations on pressures and compositions, are defined by:





_







 100/N U U_exp /U_exp

Deviation _cal (9)

The result shows a good agreement of the model with all the available experimental data. Moreover we have used the PPR78 predictive model form Privat et al. [12]. The prediction is very good and so confirms the high quality of the data.

Conclusion

In this paper we present VLE and LLE data for the system methane + H2S at 5

temperatures. We used a “static-analytic” method to obtain our experimental data. We chose the Peng-Robinson EoS, with the Mathias-Copeman alpha function and the classical mixing rules.

The experimental results are given with following maximum expanded uncertainties (k = 2): u(T) = 0.06 K, u(P) = 0.006 MPa and u(x, y) = 0.017 for vapour and liquid mole fractions. Comparisons are done with literature data and the phase diagram is determined and classified as type III according to Scott and van Konynenburg classification.

The next work will consist of a comparison of thermodynamic models frequently used for industrial applications. Equation of state combined with excess Gibbs model and Huron Vidal type mixing rule can be used to present the phase diagram of the system. Also, H2S can be considered as an associating fluid and so associative equations (like

CPA or PC-SAFT) can be used to represent the data.

Concerning the study at 186.25 K, the temperature was close to triple point temperature of H2S (190.86 K from [13], 187.62 K from [14]). Experimentally we did not

present the correct phase diagram at 186.25 K (solid – vapour equilibrium is expected at low pressures) and highlight metastability for some data. Such work will be the subject of future paper.

Acknowledgments

List of symbols:

a Parameter of the equation of state (energy parameter [J. m3.mol-2])

b Parameter of the equation of state (molar co volume parameter [m3.mol-1])

c Mathias-Copeman coefficient

F Objective function

k Binary interaction parameter

N Number of data points

P Pressure [MPa]

T Temperature [K]

x Liquid mole fraction

y Vapour mole fraction

Greek letters

 Acentric factor

Subscripts

c Critical property

cal Calculated property

exp Experimental property

i,j Molecular species

1 Methane

2 H2S

Superscript

References :

[1] H. H. Reamer and B. H. Sage, W. N. Lacey, Ind. Eng. Chem. 43 (1951), 976-981. [2] J. P. Kohn and F. Kurata, AIChE J. 4 (1958) 211-217.

[3] Yarym-Agaev, N.L., Afanasenko, L.D., Matvienko, V.G., Ukr. Khim. Zh. (Russ.Ed.), 57, 701, 1991

[4] H. Knapp, R. Döring, L. Oellrich, U. Plöcker, J. M. Prausnitz, DECHEMA Chemistry Data Series, Vol. VI, 1982, Frankfurt/Main.

[5] D.Y. Peng and D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59-64.

[6] R. L. Scott and P. H. van Konynenburg, Philos. Trans. R. Soc. 298 (1980) 495-594. [7] X. Courtial, J.C. B. Soo, C. Coquelet, P. Paricaud, D. Ramjugernath, D. Richon, Fluid Phase Equilibr. 277 (2009) 152-161

[8] P. Théveneau, C. Coquelet, D. Richon, Fluid Phase Equilibr. 249 (2006) 179-186. [9] P. Guilbot, A. Valtz, H. Legendre, D. Richon, Analusis 28 (2000) 426-431. [10] P. M. Mathias and T. W. Copeman, Fluid Phase Equilib. 13 (1983) 91-108. [11] E. R. Åberg and A. G. Gustavsson, Analytica Chimica Acta 144 (1982) 39-53. [12] R. Privat, F. Mutelet, J.N. Jaubert Ind. Eng. Chem. Res. 2008, 47, 10041–10052. [13] E. Beckmann and P. Waentig, Z. Anorg. Chem., 1910, 67, 17.

[14] W.F. Giauque and R. W.Blue, J. Am. Chem. Soc., 1936, 58, 831. [15] A. Yokozeki, Int. J. Thermophys. 24 (2003) 589–620.

List of figures

Figure 1: Flow diagram of the equipment: C: Carrier Gas, EC: Equilibrium Cell, FV: Feeding Valve, LB: Liquid Bath, LS: Liquid Sampler, PP: Platinum Probe, MC: Methane Cylinder, PT: Pressure Transducer, HC: Hydrogen sulphide Cylinder, SM: Sampler Monitoring, ST: Sapphire Tube, TCi: Thermal Compressor i, Th: Thermocouple, TR: Thermal Regulator, VP: Vacuum Pump, VS: Vapour Sampler, VSS: Variable Speed Stirring System.

Figure 2: Pressure as a function of CH4 mole fraction in the CH4 (1) + H2S (2) mixture at

186.25 K. Solid lines: calculated with PR EoS (our model) and kij = 0.099. Dashed lines:

calculated with PPR78. Symbols : Δ= experimental data, ● = pure methane vapour pressure.

Figure 3: Pressure as a function of CH4 mole fraction in the CH4 (1) + H2S (2) mixture at

203.40 K. Solid lines: calculated with PR EoS (our model), and kij = 0.098. Dashed lines:

calculated with PPR78. Symbols = experimental data.

List of tables

Table 1: Chemicals sample

Table 2: Critical parameters and acentric factors for hydrogen sulphide and methane [12] from DIPPR database

Table 3: Mathias-Copeman coefficients.

Table 4: “Vapour-liquid” and “liquid-liquid” equilibrium pressures and phase

compositions (campaign 2) for the Methane (1) - H2S (2) mixture at 186.25 and 203.40 K.

u(P, k=2) = 0.0025 MPa, u(T, k=2) = 0.02 K and u(x1, y1, k=2) = 0.010.

Table 5: “Vapour-liquid” equilibrium pressures and phase compositions (campaign 1) for the Methane (1) - H2S (2) mixture at 223.17, 273.54 and 313.08 K.

Remark: For some VLE points, only bubble pressures and liquid compositions are indicated

Table 1: Chemical

Name

Source Initial Vol. Fraction Purity Purification Method Final Mole Fraction Purity Analysis Method

Methane Air Liquide 0.99995 none - SMa

Hydrogen Sulphide

Air Liquide 0.995 none - SM

a Supplier Method

Table 2

Compound Tc/K Pc/MPa 

H2S 373.53 8.963 0.094168

Table 4

Pexp /MPa x1 y1exp

“Vapor liquid“ equilibria

T= 186.25 K

0.885 0.0173 0.9703

1.931 0.0450 0.9821

2.948 0.0709 0.9842

3.671 0.0898 0.9833

“Liquid – liquid” equilibria

P /MPa x1L1exp x1L2exp

4.970 0.0927 0.9184

6.089 0.0936 0.9135

7.407 0.0943 0.9122

8.787 0.0957 0.9080

10.364 0.0970 0.9036

“Vapor - liquid“ equilibria

T= 203.40 K 0.043 0 0 0.510 0.0091 0.8585 1.017 0.0193 0.9239 2.402 0.0502 0.9530 3.222 0.0692 0.9618 1.718 0.0350 0.9472 3.884 0.0851 0.9608 4.611 0.1030 0.9602 4.994 0.1124 0.9567 5.444 0.1213 0.9495 5.660 0.1237 0.9320 5.830 0.1255 0.9038

“Liquid – liquid” equilibria

P /MPa x1L1exp x1L2exp

6.737 0.1305 0.8806

7.915 0.1354 0.8714

8.964 0.1387 0.8629

9.859 0.1394 0.8577

Table 5:

Pexp /MPa x1 y1exp

Table 7: References T /K or range of T /K Dev. %, P Dev. % Y (CH4) Dev. % Y (H2S)

This work ; kij from table 6

186.90* 6.0 0.2 5.9

203.40* 11.1 0.8 14.6

223.17 4.3 1.2 4.2

273.54 4.9 2.7 5.7

313.08 5.0 3.6 2.1

This work ; kij given by eq. 7 [186 – 313] 10.3 2.6 16.9